%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB065+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:47 AM UTC 2025
% Result : Theorem 0.47s 0.69s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWB065+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 07:57:26 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.47/0.69 % SZS status Theorem
% 0.47/0.69 % SZS output start Proof
% 0.47/0.69 tff(uri_ex_u_type, type, (
% 0.47/0.69 uri_ex_u: $i)).
% 0.47/0.69 tff(uri_ex_w_type, type, (
% 0.47/0.69 uri_ex_w: $i)).
% 0.47/0.69 tff(icext_type, type, (
% 0.47/0.69 icext: ( $i * $i ) > $o)).
% 0.47/0.69 tff(tptp_fun_X1_140_type, type, (
% 0.47/0.69 tptp_fun_X1_140: $i)).
% 0.47/0.69 tff(iext_type, type, (
% 0.47/0.69 iext: ( $i * $i * $i ) > $o)).
% 0.47/0.69 tff(uri_rdf_type_type, type, (
% 0.47/0.69 uri_rdf_type: $i)).
% 0.47/0.69 tff(tptp_fun_X0_141_type, type, (
% 0.47/0.69 tptp_fun_X0_141: $i)).
% 0.47/0.69 tff(uri_owl_oneOf_type, type, (
% 0.47/0.69 uri_owl_oneOf: $i)).
% 0.47/0.69 tff(uri_rdf_nil_type, type, (
% 0.47/0.69 uri_rdf_nil: $i)).
% 0.47/0.69 tff(uri_rdf_rest_type, type, (
% 0.47/0.69 uri_rdf_rest: $i)).
% 0.47/0.69 tff(uri_rdf_first_type, type, (
% 0.47/0.69 uri_rdf_first: $i)).
% 0.47/0.69 tff(uri_owl_sameAs_type, type, (
% 0.47/0.69 uri_owl_sameAs: $i)).
% 0.47/0.69 tff(ic_type, type, (
% 0.47/0.69 ic: $i > $o)).
% 0.47/0.69 tff(tptp_fun_X_8_type, type, (
% 0.47/0.69 tptp_fun_X_8: ( $i * $i ) > $i)).
% 0.47/0.69 tff(1,plain,
% 0.47/0.69 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(2,plain,
% 0.47/0.69 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.47/0.69 tff(3,plain,
% 0.47/0.69 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(4,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.47/0.69 tff(5,plain,
% 0.47/0.69 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.47/0.69 tff(6,plain,(
% 0.47/0.69 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.47/0.69 inference(skolemize,[status(sab)],[5])).
% 0.47/0.69 tff(7,plain,
% 0.47/0.69 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.47/0.69 tff(8,plain,
% 0.47/0.69 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, uri_ex_w, X1!140) <=> icext(X1!140, uri_ex_w))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(9,plain,
% 0.47/0.69 (iext(uri_rdf_type, uri_ex_w, X1!140) <=> icext(X1!140, uri_ex_w)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.47/0.69 tff(10,plain,
% 0.47/0.69 (?[X0: $i, X1: $i] : (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1)) <=> ?[X0: $i, X1: $i] : (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(11,plain,
% 0.47/0.69 (^[X0: $i, X1: $i] : trans(monotonicity(rewrite(((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) <=> (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0))), ((((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_rdf_type, uri_ex_w, X1)) <=> ((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_rdf_type, uri_ex_w, X1)))), rewrite(((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_rdf_type, uri_ex_w, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1))), ((((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_rdf_type, uri_ex_w, X1)) <=> (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(12,plain,
% 0.47/0.69 (?[X0: $i, X1: $i] : (((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_rdf_type, uri_ex_w, X1)) <=> ?[X0: $i, X1: $i] : (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[11])).
% 0.47/0.69 tff(13,axiom,(?[X0: $i, X1: $i] : (((iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_oneOf, X1, X0)) & iext(uri_rdf_type, uri_ex_w, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_rdfbased_sem_eqdis_sameas_ext')).
% 0.47/0.69 tff(14,plain,
% 0.47/0.69 (?[X0: $i, X1: $i] : (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.47/0.69 tff(15,plain,
% 0.47/0.69 (?[X0: $i, X1: $i] : (iext(uri_rdf_first, X0, uri_ex_u) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_oneOf, X1, X0) & iext(uri_rdf_type, uri_ex_w, X1))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.47/0.69 tff(16,plain,(
% 0.47/0.69 iext(uri_rdf_first, X0!141, uri_ex_u) & iext(uri_rdf_rest, X0!141, uri_rdf_nil) & iext(uri_owl_oneOf, X1!140, X0!141) & iext(uri_rdf_type, uri_ex_w, X1!140)),
% 0.47/0.69 inference(skolemize,[status(sab)],[15])).
% 0.47/0.69 tff(17,plain,
% 0.47/0.69 (iext(uri_rdf_type, uri_ex_w, X1!140)),
% 0.47/0.69 inference(and_elim,[status(thm)],[16])).
% 0.47/0.69 tff(18,plain,
% 0.47/0.69 ((~(iext(uri_rdf_type, uri_ex_w, X1!140) <=> icext(X1!140, uri_ex_w))) | (~iext(uri_rdf_type, uri_ex_w, X1!140)) | icext(X1!140, uri_ex_w)),
% 0.47/0.69 inference(tautology,[status(thm)],[])).
% 0.47/0.69 tff(19,plain,
% 0.47/0.69 ((~(iext(uri_rdf_type, uri_ex_w, X1!140) <=> icext(X1!140, uri_ex_w))) | icext(X1!140, uri_ex_w)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.47/0.69 tff(20,plain,
% 0.47/0.69 (icext(X1!140, uri_ex_w)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[19, 9])).
% 0.47/0.69 tff(21,plain,
% 0.47/0.69 (^[X: $i, Y: $i] : refl((iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> (iext(uri_owl_sameAs, X, Y) <=> (X = Y)))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(22,plain,
% 0.47/0.69 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[21])).
% 0.47/0.69 tff(23,plain,
% 0.47/0.69 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y)) <=> ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(24,axiom,(![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_sameas')).
% 0.47/0.69 tff(25,plain,
% 0.47/0.69 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.47/0.69 tff(26,plain,(
% 0.47/0.69 ![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.47/0.69 inference(skolemize,[status(sab)],[25])).
% 0.47/0.69 tff(27,plain,
% 0.47/0.69 (![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.47/0.69 tff(28,plain,
% 0.47/0.69 ((~![X: $i, Y: $i] : (iext(uri_owl_sameAs, X, Y) <=> (X = Y))) | (iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) <=> (uri_ex_w = uri_ex_u))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(29,plain,
% 0.47/0.69 (iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) <=> (uri_ex_w = uri_ex_u)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.47/0.69 tff(30,plain,
% 0.47/0.69 ((~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)) <=> (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(31,axiom,(~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion_rdfbased_sem_eqdis_sameas_ext')).
% 0.47/0.69 tff(32,plain,
% 0.47/0.69 (~iext(uri_owl_sameAs, uri_ex_w, uri_ex_u)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.47/0.69 tff(33,plain,
% 0.47/0.69 ((~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) <=> (uri_ex_w = uri_ex_u))) | iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) | (~(uri_ex_w = uri_ex_u))),
% 0.47/0.69 inference(tautology,[status(thm)],[])).
% 0.47/0.69 tff(34,plain,
% 0.47/0.69 ((~(iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) <=> (uri_ex_w = uri_ex_u))) | (~(uri_ex_w = uri_ex_u))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.47/0.69 tff(35,plain,
% 0.47/0.69 (~(uri_ex_w = uri_ex_u)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[34, 29])).
% 0.47/0.69 tff(36,plain,
% 0.47/0.69 ((~(icext(X1!140, uri_ex_w) <=> (uri_ex_w = uri_ex_u))) | (~icext(X1!140, uri_ex_w)) | (uri_ex_w = uri_ex_u)),
% 0.47/0.69 inference(tautology,[status(thm)],[])).
% 0.47/0.69 tff(37,plain,
% 0.47/0.69 (~(icext(X1!140, uri_ex_w) <=> (uri_ex_w = uri_ex_u))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[36, 35, 20])).
% 0.47/0.69 tff(38,plain,
% 0.47/0.69 (iext(uri_rdf_rest, X0!141, uri_rdf_nil)),
% 0.47/0.69 inference(and_elim,[status(thm)],[16])).
% 0.47/0.69 tff(39,plain,
% 0.47/0.69 (iext(uri_rdf_first, X0!141, uri_ex_u)),
% 0.47/0.69 inference(and_elim,[status(thm)],[16])).
% 0.47/0.69 tff(40,plain,
% 0.47/0.69 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))))))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(41,plain,
% 0.47/0.69 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[40])).
% 0.47/0.69 tff(42,plain,
% 0.47/0.69 (^[Z: $i, S1: $i, A1: $i] : refl(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(43,plain,
% 0.47/0.69 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[42])).
% 0.47/0.69 tff(44,plain,
% 0.47/0.69 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(45,plain,
% 0.47/0.69 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[44])).
% 0.47/0.69 tff(46,plain,
% 0.47/0.69 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[45, 43])).
% 0.47/0.69 tff(47,plain,
% 0.47/0.69 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> ((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))) <=> (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))), rewrite((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))), ((iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))), rewrite((((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1)))))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))), ((((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) <=> (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))) <=> (((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))))), rewrite((((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))) <=> ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(48,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[47])).
% 0.47/0.70 tff(49,plain,
% 0.47/0.70 (^[Z: $i, S1: $i, A1: $i] : rewrite(((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(50,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[49])).
% 0.47/0.70 tff(51,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(52,plain,
% 0.47/0.70 (^[Z: $i, S1: $i, A1: $i] : trans(monotonicity(monotonicity(rewrite((ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))), ((iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) <=> (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), (((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))))),
% 0.47/0.70 inference(bind,[status(th)],[])).
% 0.47/0.70 tff(53,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1))))) <=> ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.47/0.70 inference(quant_intro,[status(thm)],[52])).
% 0.47/0.70 tff(54,axiom,(![Z: $i, S1: $i, A1: $i] : ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_enum_class_001')).
% 0.47/0.70 tff(55,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.47/0.70 tff(56,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_oneOf, Z, S1) <=> (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.47/0.70 tff(57,plain,(
% 0.47/0.70 ![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | ((~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1)))))))),
% 0.47/0.70 inference(skolemize,[status(sab)],[56])).
% 0.47/0.70 tff(58,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_oneOf, Z, S1)) | (ic(Z) & ![X: $i] : (icext(Z, X) <=> (X = A1)))) & (iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.47/0.70 tff(59,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.47/0.70 tff(60,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))) | (~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.47/0.70 tff(61,plain,
% 0.47/0.70 (![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[60, 41])).
% 0.47/0.70 tff(62,plain,
% 0.47/0.70 (((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_u)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!140, X0!141) | (~ic(X1!140)) | (~(icext(X1!140, tptp_fun_X_8(uri_ex_u, X1!140)) <=> (tptp_fun_X_8(uri_ex_u, X1!140) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))))))) <=> ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X0!141, uri_ex_u)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!140, X0!141) | (~ic(X1!140)) | (~(icext(X1!140, tptp_fun_X_8(uri_ex_u, X1!140)) <=> (tptp_fun_X_8(uri_ex_u, X1!140) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(63,plain,
% 0.47/0.70 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_u)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!140, X0!141) | (~ic(X1!140)) | (~(icext(X1!140, tptp_fun_X_8(uri_ex_u, X1!140)) <=> (tptp_fun_X_8(uri_ex_u, X1!140) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))))))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(64,plain,
% 0.47/0.70 ((~![Z: $i, S1: $i, A1: $i] : ((~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, Z, S1) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_8(A1, Z)) <=> (tptp_fun_X_8(A1, Z) = A1))))) | (~((~iext(uri_owl_oneOf, Z, S1)) | (~((~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (X = A1))))))))))) | (~iext(uri_rdf_first, X0!141, uri_ex_u)) | (~iext(uri_rdf_rest, X0!141, uri_rdf_nil)) | (~((~(iext(uri_owl_oneOf, X1!140, X0!141) | (~ic(X1!140)) | (~(icext(X1!140, tptp_fun_X_8(uri_ex_u, X1!140)) <=> (tptp_fun_X_8(uri_ex_u, X1!140) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u)))))))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.47/0.70 tff(65,plain,
% 0.47/0.70 (~((~(iext(uri_owl_oneOf, X1!140, X0!141) | (~ic(X1!140)) | (~(icext(X1!140, tptp_fun_X_8(uri_ex_u, X1!140)) <=> (tptp_fun_X_8(uri_ex_u, X1!140) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[64, 61, 39, 38])).
% 0.47/0.70 tff(66,plain,
% 0.47/0.70 (((~(iext(uri_owl_oneOf, X1!140, X0!141) | (~ic(X1!140)) | (~(icext(X1!140, tptp_fun_X_8(uri_ex_u, X1!140)) <=> (tptp_fun_X_8(uri_ex_u, X1!140) = uri_ex_u))))) | (~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u)))))))) | ((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(67,plain,
% 0.47/0.72 ((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u)))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.47/0.72 tff(68,plain,
% 0.47/0.72 (iext(uri_owl_oneOf, X1!140, X0!141)),
% 0.47/0.72 inference(and_elim,[status(thm)],[16])).
% 0.47/0.72 tff(69,plain,
% 0.47/0.72 ((~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))) | (~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u)))))),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(70,plain,
% 0.47/0.72 ((~((~iext(uri_owl_oneOf, X1!140, X0!141)) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))))) | (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u)))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.47/0.72 tff(71,plain,
% 0.47/0.72 (~((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.47/0.72 tff(72,plain,
% 0.47/0.72 (((~ic(X1!140)) | (~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u)))) | ![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))),
% 0.47/0.72 inference(tautology,[status(thm)],[])).
% 0.47/0.72 tff(73,plain,
% 0.47/0.72 (![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.47/0.72 tff(74,plain,
% 0.47/0.72 ((~![X: $i] : (icext(X1!140, X) <=> (X = uri_ex_u))) | (icext(X1!140, uri_ex_w) <=> (uri_ex_w = uri_ex_u))),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(75,plain,
% 0.47/0.72 ($false),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[74, 73, 37])).
% 0.47/0.72 % SZS output end Proof
% 0.47/0.72 % E exiting
%------------------------------------------------------------------------------